As a commonly applied technique for imaging seismic data, conventional tilted transverse isotropic (“TTI”) reverse time migration (“RTM”) (collectively “TTI-RTM”) propagates a source wave field forward in time and a receiver wave field backward in time to image the subsurface reflector by any well-known two-way wave equation such as the two-way wave equation described in the paper “Reverse Time Migration: Geophysics” by Baysal, et al. and in the paper “Migration by Extrapolation of Time-Dependent Boundary Values: Geophysical Prospecting” by G. A. McMechan. Although wave equation migration and/or reverse time migration are referred to herein as two-way, they may also be referred to as full-way. In the paper “Acoustic Approximations for Processing in Transversely Isotropic Media” by T. Aikhalifah, for example, conventional TTI-RTM is referenced to propose a pseudo-acoustic approximation in transversely isotropic media with a vertical axis (“VTI”). Based on the pseudo-acoustic approximation in VTI media, research such as, for example, that described in the papers “An Anisotropic Acoustic Wave Equation for Modeling and Migration in 2D TTI Media” by Zhou, et al. and “Reverse Time Migration in Tilted Transversely Isotropic (TTI) Media” by Fletcher, et al. extended this approximation from VTI to TTI media. These techniques enable structures with strong anisotropy to be imaged. Although conventional TTI-RTM has been applied widely, the computation cost and storage for wavefields are still disadvantages for current computer systems. In other words, the computation cost and memory requirement are still problems for large dataset migration, especially for three-dimensional (“3D”) conventional TTI-RTM.
Instead of a two-way wave equation associated with conventional TTI-RTM, a one-way wave equation can provide faster processing and handle strong lateral velocity variation. One-way wave equations, such as a Finite Difference propagator, a Phase-Shift-Plus-Interpolation propagator, and/or a Generalized Screen propagator, demonstrate good accuracy in general. By extending the one-way isotropic wave equation migration (“WEM”) to TTI-WEM as described in the papers “3D Wavefield Extrapolation in Laterally Varying Tilted TI Media” by San, et al., “Implicit Wave Equation Migration in TTI Media Using High Order Operators” by A. A. Valenciano, and “3D TTI Implicit Finite Difference Migration With Nonlinear Optimized Four-Direction Splitting Expansion” by Hua, et al., one-way WEM is able to produce an anisotropic image with high efficiency. Nevertheless, because the one-way WEM ignores up-going waves, one-way WEM fails to handle extremely complex structures, such as steeply dip events and overturned reflectors.
To combine the advantages of one-way WEM and two-way WEM, a hybrid propagator for prestack migration in isotropic media was developed and is described in the paper “Hybrid One-Way and Full-Way Wave Equation Propagator and Prestack Migration” by Luo and Jin (“Luo and Jin”) The hybrid propagator combines one-way and two-way WEM to extrapolate a wavefield progressively. In this manner, a one-way propagator may be applied to less complex media while the two-way propagator may be applied to extremely complicated media. Although the use of the Luo and Jin hybrid propagator in isotropic media generates comparable image results with two-way WEM for RTM with less noise and computational costs, it has not been applied to TTI media. Moreover, the Luo and Jin hybrid propagator does not contemplate the use of Pade approximation, which could provide maximum accuracy for wave propagation.